Dr Sigrid Lipka

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• Todays Topics
• Deductive reasoning Reasoning from evidence to
  conclusions.
• Deduction logic
• Experimental studies of deductive reasoning
• Theories of deductive reasoning.

• Dr Sigrid Lipka
• s.lipka_at_derby.ac.uk
• Recommended Reading
• Eysenck, M. W., Keane M. T. (2001). Cognitive
  psychology. Hove Psychology Press.
• Johnson-Laird, P. Byrne,R. (1991). Deduction.
  London Psychology Press.
• Manktelow, K. (1999). Reasoning and Thinking.
  Hove Psychology Press.

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• Deductive reasoning
• A good detective examines the evidence and uses
  it to formulate conclusions.
• Deductive refers to process of taking two or more
  pieces of evidence (premises) and combining these
  to form logically valid conclusion.
• Called inference.

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• Reasoning logic
• Logic is used to formalise reasoning.
• Logic specifies rules of inference conclusion
  always true if
• It follows from rule of inference.
• Premises are true.

• Logic as normative theory
• Logic adopted as normative theory or benchmark
  for human reasoning.
• Experimenters examine whether we reason logically
  and attempt to account for deviations from
  logical performance.

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• Implication
• IF p THEN q
• Negation
• NOT p
• CONJUNCTION
• p AND q
• DISJUNCTION
• p OR q

• Propositional logic
• Simple forms of logic
• Provides rules about reasoning with statements
  that are connected using following operators
• IF . . . THEN
• NOT
• AND
• OR

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• Conditional reasoning
• Reasoning with IF . . .THEN statements
• Conditional statements have 2 parts
• Antecedent often called p, consequent often
  called q.
• Statement sometimes read as p implies q.

• IF you revise THEN you will pass your
  exams.
• p q
• ANTECEDENT CONSEQUENT

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• Rules of inference for conditional reasoning.
• There are two valid rules of inference, and two
  logical fallacies in conditional reasoning.
• Valid inferences conclusions that are
  necessarily true (i.e. must be true) according to
  logic.

• Logical fallacy a conclusion that is invalid
  (i.e. demonstrably false) according to the rules
  of inference.
• Important Validity only depends on the rules of
  inference and not on whether the conclusion is
  actually true.

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• Rules of inference for conditional reasoning.
• Modus ponens is a logically valid rule of
  inference.
• If p is true
• then following rules of logic
• q must also be true.

• Premise 1
• IF you revise, THEN you will pass your exams.
• Premise 2
• You do revise.
• Conclusion
• Therefore, you will pass your exams.

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• Rules of inference for conditional reasoning.
• Modus tollens is also a logically valid rule of
  inference.
• If q is NOT true
• then following rules of logic
• p must also NOT be true.

• Premise 1
• IF you revise, THEN you will pass your exams.
• Premise 2
• You do not pass your exams.
• Conclusion
• Therefore, you did not revise.

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• Logical fallacies
• Affirmation of the consequent is not a logically
  valid rule of inference.
• If p then q
• q
• Therefore p
• INVALID INFERENCE

• Premise 1
• IF you revise, THEN you will pass your exams.
• Premise 2
• You pass your exams.
• Invalid Conclusion
• Therefore, you must have revised.
• (NO! You might pass exam for some other reason)

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• Logical fallacies
• Denial of the antecedent also is not a logically
  valid rule of inference.
• If p then q
• not p
• Therefore not q
• INVALID INFERENCE

• Premise 1
• IF you revise, THEN you will pass your exams.
• Premise 2
• You did not revise.
• Conclusion
• Therefore, you will not pass your exams.
• (NO! You might pass exam for some other reason)

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• Do people reason logically?
• Test this by presenting PPs with sets of premises
  and examining what conclusions they produce.
• Evans (1983) found low rate of valid modus
  tollens inferences, and high rate of invalid
  inferences

• How do theories of conditional reasoning explain
  this pattern of results?

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• Why do people make logical reasoning errors?
• 1. People dont reason by following rules of
  logic!
• 2. Mental logic theories (e.g. Braine OBrien,
  1991 Rips, 1994) People reason logically, but
  make errors because of limited memory capacity,
  or because they lack particular rule of
  inference.
• 3. Mental models theory People reason logically,
  but not by applying rules of inference to
  premises. Errors are result of limited cognitive
  resources.

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• Mental logic theories
• Claim that we have rules of logic in our head.
• Apply these rules to sets of premises.
• Errors due to lack of working memory capacity, or
  lack of a specific rule.
• E.g. System lacks MT rule and takes more error-
  prone route to producing conclusion.

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• Mental models theory (Johnson-Laird Byrne,
  1991)
• Build model of situation described by premises.
  
• Initial model contains only information made
  explicit in premises (this is important later).
• Mental inspection of model produces conclusion.
• Test conclusion by attempting to construct
  alternative models for which this conclusion is
  false.

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• What mental models look like

IF P then Q p q p means
that there are no other ps. That is p cannot
be added without a q opposite. means that
other information can be added to the model.
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• Mental Models account of Modus Ponens
• If you revise, then you will pass the exam.
• You do revise.

IF P then Q p q P is
true p full model p q conclusion q
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• Mental Models account of Modus Tollens
• If you revise , then you will pass the exam.
• You do not pass the exam.

Stage 1
Build model for IFTHEN rule IF P then
Q p q
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• Mental Models account of Modus Tollens
• If you revise then you will pass the exam.
• You do not pass the exam.

Stage 2
Add second premise IF P then Q p q Not q
q
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• Mental Models account of Modus Tollens
• Tricky bit Remember p means there are no ps
  without q. So what goes opposite NOT q?

Stage 3
Expanded model IF P then Q p q Not q
p q Conclusion p
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• Summary of theoretical accounts

• Mental logic
• Formal account people reason by applying rules
  of logic.
• Errors occur because of cognitive limitations, or
  because we lack specific rules.

• Mental models
• Semantic account people reason by constructing
  abstract models of situation.
• Errors occur because of cognitive limitations.
• People often fail to expand initial models.

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• Applications

• Where do you think deductive reasoning might be
  important?
• Detective work
• Medical reasoning
• Scientific research
• Engineering design

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• Summary

• Logic provides benchmark for testing deductive
  reasoning abilities.
• People make errors on simple conditional
  reasoning tasks.
• Psychological theories must explain why these
  errors are made we considered Mental Logic
  Mental Models accounts.
• Studying improving deductive reasoning is
  important for several domains.